Stochastic User Equilibrium Traffic Assignment with Turn‐delays in Intersections

Abstract

Turn‐delays in intersections contribute significantly to travel times and thus route choices in urban networks. However, turns are difficult to handle in traffic assignment models due to the asymmetric Jacobian in the cost functions. The paper describes a model where turn delays have been included in the solution algorithm of Stochastic User Equilibrium (SUE) traffic assignment. When the Jacobian is symmetric, SUE minimises the road users' ‘perceived travel resistances’. This is a probit‐model where the links cost‐functions of the links are traffic dependent. Hereby, overlapping routes are handled in a consistent way. However, no theoretical proof of convergence has been given if the Jacobian is asymmetric, although convergence can be shown probable for model data representing realistic road‐networks. However, according to the authors knowledge SUE with intersection delays have not been tested earlier on a full‐scale network. Therefore, an essential part of the paper presents practical tests of convergence. Both geometric delays and delays caused by other turns are considered for each turn. Signalised and non‐signalised intersections are handled in different ways, as are roundabouts. In signalised intersections a separate model handles queues longer than one green‐period. Green‐waves can also be taken into consideration. The model has been tested on a large‐scale network for Copenhagen with good results. To make it possible to establish the comprehensive data, a GIS‐based ‘expert system’ was implemented (see Nielsen, O.A., Frederiksen, R. D. and Simonsen, N. (1997). Using expert system rules to establish data on intersections and turns in road networks. International Transactions in Operational Research , 5 , 513–529.